Two conducting wires of the same material and of equal lengths and equal diameters are first connected in parallel and then in series in a circuit across the same potential difference. The ratio of heat produced in parallel and series combinations is

Let the resistance of each wire be R. In parallel combination, R_p = R/2; in series combination, R_s = 2R. Heat produced at constant potential difference V is H = V²t/R. Therefore H_p/H_s = R_s/R_p = (2R)/(R/2) = 4. So the ratio of heat produced in parallel to series is 4:1. Parallel combination produces more heat because the equivalent resistance is lower, allowing more current to flow at the same voltage.